CIE, IGCSE, 0606/11, Additional Maths, Jun19

This document consists of 15 printed pages and 1 blank page.

DC (CE/CB) 165273/2© UCLES 2019 [Turn over

*2049112309*

ADDITIONAL MATHEMATICS 0606/11Paper 1 May/June 2019 2 hoursCandidates answer on the Question Paper.Additional Materials: Electronic calculator

READ THESE INSTRUCTIONS FIRST

Write your centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use an HB pencil for any diagrams or graphs.Do not use staples, paper clips, glue or correction fluid.DO NOT WRITE IN ANY BARCODES.

Answer all the questions.Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.The use of an electronic calculator is expected, where appropriate.You are reminded of the need for clear presentation in your answers.

At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks for this paper is 80.

Cambridge Assessment International EducationCambridge International General Certificate of Secondary Education

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Mathematical Formulae

1. ALGEBRA

Quadratic Equation

For the equation ax2 + bx + c = 0,

x ab b ac

242!

=- -

Binomial Theorem

(a + b)n = an + (n1 )an–1 b + ( n2 )an–2 b2 + … + ( n

r )an–r br + … + bn,

where n is a positive integer and ( nr ) = n!

(n – r)!r!

2. TRIGONOMETRY

Identities

sin2 A + cos2 A = 1

sec2 A = 1 + tan2 A

cosec2 A = 1 + cot2 A

Formulae for ∆ABCa

sin A = b

sin B = c

sin C

a2 = b2 + c2 – 2bc cos A

∆ = 1 2 bc sin A


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1 (a) On the Venn diagrams below, shade the region indicated.

A B

C

A B

C

� �

( )A B C+ , ( )'A B C, +

[2]

(b) On the Venn diagram below, draw sets P, Q and R such that

P R1 , Q R1 and P Q+ Q= .

[2]


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2 (i) Write down the amplitude of sin x4 3 1- . [1]

(ii) Write down the period of sin x4 3 1- . [1]

(iii) On the axes below, sketch the graph of siny x4 3 1= - for ° ° °x90 90G G- .

6

4

2

–90 –60 –30 0 30 60 90

–2

–4

–6

y

x

[3]


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3 The polynomial ( ) ( ) ( )x x x k2 1 12p = - + - , where k is a constant.

(i) Write down the value of ( )kp - . [1]

When p(x) is divided by x + 3 the remainder is 23.

(ii) Find the value of k. [2]

(iii) Using your value of k, show that the equation ( )x 25p =- has no real solutions. [3]


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4 (i) The first 3 terms, in ascending powers of x, in the expansion of bx28

+` j can be written as a + 256x + cx2. Find the value of each of the constants a, b and c. [4]

(ii) Using the values found in part (i), find the term independent of x in the expansion of

bx x x2 2 3 28+ -` bj l . [3]


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5 A particle P is moving with a velocity of 20 ms-1 in the same direction as 43e o.

(i) Find the velocity vector of P. [2]

At time t = 0 s, P has position vector 21e o relative to a fixed point O.

(ii) Write down the position vector of P after t s. [2]

A particle Q has position vector 1817e o relative to O at time t = 0 s and has a velocity vector 12

8e o ms-1.

(iii) Given that P and Q collide, find the value of t when they collide and the position vector of the point of collision. [3]


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6y

x

P

O

Qy x x3 2 12= - +

y x2 5= +

The diagram shows the curve y x x3 2 12= - + and the straight line y x2 5= + intersecting at the points P and Q. Showing all your working, find the area of the shaded region. [8]


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7 (a) Solve log logx x 123 9+ = . [3]

(b) Solve ( ) (log logy3 10 2 21

42

4- = )y 1- + . [5]


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8 It is given that ( )x 5 1f ex= - for x Rd .

(i) Write down the range of f. [1]

(ii) Find f -1 and state its domain. [3]

It is given also that ( )x x 4g 2= + for x Rd .

(iii) Find the value of fg(1). [2]


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(iv) Find the exact solutions of ( )x 40g2 = . [3]


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9 In this question all lengths are in centimetres.

A closed cylinder has base radius r, height h and volume V. It is given that the total surface area of the cylinder is 600r and that V, r and h can vary.

(i) Show that V r r300 3r r= - . [3]

(ii) Find the stationary value of V and determine its nature. [5]


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10 When lg y is plotted against x2 a straight line graph is obtained which passes through the points (2, 4) and (6, 16).

(i) Show that y 10A Bx2

= + , where A and B are constants. [4]

(ii) Find y when x3

1= . [2]

(iii) Find the positive value of x when y = 2. [3]


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11 It is given that y x x1 2 32 21

= + -` `j j .

(i) Show that xy

x

Px Qx

2 3

1dd

21

2

=

-

+ +

` j, where P and Q are integers. [5]


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(ii) Hence find the equation of the normal to the curve y x x1 2 32 21

= + -` `j j at the point where x = 2, giving your answer in the form ax + by + c = 0, where a, b and c are integers. [4]


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CIE, IGCSE, 0606/11, Additional Maths, Jun19